Yimin Jin

Mathematical description of differential scanning calorimetry based on periodic temperature modulation

Abstract The changes needed in the mathematical description of differential scanning calorimetry caused by periodical modulation of temperature are presented. Calibration procedures and possible extensions of the method are suggested, all based on the model of scanning calorimetry without temperature gradient within the sample. The basic differential equation for heat flow under modulation conditions is solved and the steady state identified. The main advantage of modulated differential thermal analysis is the elimination of nonperiodic heat losses and gains. It is suggested that the precision of heat capacity measurement may be increased by a factor of 10 using proper calibration. The thermal analysis in transition regions is discussed.

Heat capacity measurement by modulated DSC at constant temperature

The mathematical equations for step-wise measurement of heat capacity (Cp) by modulated differential scanning calorimetry (MDSC) are discussed for the conditions of negligible temperature gradients within sample and reference. Using a commercial MDSC, applications are evaluated and the limits explored. This new technique permits the determination ofCp by keeping the sample continually close to equilibrium, a condition conventional DSC is unable to meet. Heat capacity is measured at ‘practically isothermal condition’ (often changing not more than ±1 K). The method provides data with good precision. The effects of sample mass, amplitude and frequency of temperature modulation were studied and methods for optimizing the instrument are proposed. The correction for the differences in sample and reference heating rates, needed for high-precision data by standard DSC, do not apply for this method.ZusammenfassungDie mathematischen Gleichungen für die stufenweise Messung der Wärmekapazität (Cp) mit modulierter Differential kalorimetrie (MDSC) werden für die Bedingung eines vernachlässigbar kleinen Temperaturgradierten in Probe und Referenzsubstanz diskutiert. Diese neue Technik ermöglicht die Bestimmung vonCp ohne die Probe wesentlich vom Gleichgewicht zu entfernen, eine Bedingung die conventionelles DSC nicht erreichen kann. Die Wärmekapazität is unter “praktisch isothermer Bedingung” gemessen worden (haäfig innerhalb ±1 K). Diese Methode gibt Daten von guter Qualität. Die Effekte der Probenmasse, Amplitude und Frequenz der Temperaturmodulation wurden untersucht und Methoden für die Optimirung des Instruments werden vorgeschlagen. Die Korrekturen für Unterschiede zwischen Proben-und Refernztemparatur aufheizgeschwindigkeiten die für das normale DSC für Daten von hoher Qualität gebraucht werden, sind für diese Methode nicht nötig.

Condis Crystals of Small Molecules V. Solid State 13C NMR and Thermal Properties of N,N′-b/s(4-n-Octyloxybenzal)-1,4-Phenylenediamine (OOBPD)

Abstract Motion in the condis and liquid crystalline phases of N,N′-bis(4-n-octyloxybenzai)-4-phenylenediamine (OOBPD) over the temperature range 187-431 K has been analyzed by solid state 13C nuclear magnetic resonance under the conditions of cross-polarization transfer and magic angle spinning (CP-MAS), and 13C spin-lattice relaxation times. The 13C γ-gauche effect indicated that even in the crystals of K3 (below 385 K) conformational disorder and motion exist in the paraffin chains. Also, below the first transition temperature (K3 to K2, at 385 K), coalescence of signals suggest 180° phenylene ring flips without increase in disorder (entropy). The mobilities are evaluated using the relaxation times of “C. Heat and entropy have been determined from 130 to 550 K. From a fit of the heat capacity at low temperature to an approximate vibrational spectrum, it could be derived that a large amount of conformational entropy is introduced gradually. Corrected thermal data are given for all phase transitions. A f...

Heat capacities and transitions in n-perfluoroalkanes and poly(tetrafluoroethylene)

Abstract Heat capacities and transitions of perfluorododecane (C 12 F 26 ), perfluorotetradecane (C 14 F 30 ), perfluorohexadecane (C 16 F 34 ), perfluoroeicosane (C 20 F 42 ) and perfluorotetracosane (C 24 F 50 ) were measured by adiabatic calorimetry and differential scanning calorimetry from 5 K up to the melt. The heat capacities of the homologous series of perfluoroalkanes from n -octafluoropropane to poly(tetrafluoroethylene) in the solid state are analyzed using the Advanced THermal Analysis System (ATHAS) developed for linear macromolecules. All of the n -perfluoroalkanes show solid—mesophase transitions before the melting transition. The mesophases of short chain-length molecules can be identified as plastic crystalline (CF 4 to C 3 F 8 ). After a group of intermediate length (C 4 F 10 to C 12 F 26 ), the entropies of the solid—mesophase and isotropization transitions of the n -perfluoroalkanes approach the value of poly(tetrafluoroethylene) when expressed per mole of carbon atoms. Based on the measured heat capacities, it is possible to predict also the thermodynamic properties of the n -perfluoroalkanes not measured. Both disordering transition and isotropization temperature in the n -perfluoroalkanes with more than 12 carbon atoms can be expressed in functional form ( T d = 295( n −1.55)/( n + 7.55) and T i = 605( n −3.56)/( n + 2.75), both in kelvin).

Thermodynamic Characterization of the Plastic Crystal and Non-Plastic Crystal Phases of C70

Abstract Heat capacity measurements were performed on chromatographically purified C70 from 120 to 560 K by DSC. The experimental values were linked to the vibrational heat capacity, calculated based on normal-mode vibration frequencies available from the literature. Good agreement is found, as prior for C60 Major orientational disorder is introduced in two closely spaced transitions, reflecting the change to the phase that displays anisotropic rotation of the rugby-ball shaped molecules. The total entropy of the disordering transitions is 22.4 J/(Kmol), slightly lower than that of C60, but additional entropy is gradually acquired between 120 K and the transition temperature, making the total entropy gain higher than that of C60, as expected for a less symmetric molecule. The Debye temperature for the six lattice vibrations of C70 was calculated to be 45 K, compared to 53 K for C60 No melting temperature could be detected for C70 up to 950 K, but the entropy of fusion is estimated to be 12 J/(K mol). Enth...

Condis Crystals of Small Molecule VI. The Differences Between Smectic and Condis Phases, Evaluated by a Solid State 13C NMR Study of N,N′-bis(4-n-octyloxybenzal)-1,4-phenylenediamine (OOBPD)

Abstract Carbon-13 NMR spectra have been obtained for N,N′-bis(4-n-octyloxybenzal)-1,4-phenylenediamine (OOBPD) in the condis and smectic phases. Sharp, well-resolved spectra were obtained without magic angle sample spinning in the smectic phases under the conditions of cross-polarization or single carbon pulse followed by high-power proton decoupling. The smectic I-to-smectic C transition involves a discontinuous change in 13C chemical shifts due to a large degree to orientational disordering. Similar behavior was found between the spectra of smectic C and the isotopic state. Order parameters for various smectic phases are calculated based on the observed differences in 13C chemical shift between the isotropic state and the smectic phase. The spectra were measured at different sample orientation with respect to the external magnetic field, and show that reorienting the smectic molecules in a magnetic field is facile. Larger difference can be found between the spectra obtained by cross polarization and th...

Single-run heat capacity measurement by DSC: principle, experimental and data analysis

Abstract A single-run heat capacity measurement has been proposed based on standard heat-conduction-type differential scanning calorimetry (DSC) equipment. The experimental tests were in the range 130–560 K. The equipment used was the dual sample DSC and autosampler from TA Instruments. The RMS error of all measurements when compared to well-established adiabatic calorimetry is

Heat capacities of aliphatic and aromatic polysulphones

Abstract Heat capacities were measured for three aromatic polysulphones: poly(1,4-phenylene sulphonyl), PAS; poly(oxy-1,4-phenylene-sulphonyl-1,4-phenylene), PPES; and poly[oxy-1,4-phenylene-sulphonyl-1,4-phenylene-oxy-1,4-phenylene-(1-methylidene)-1,4-phenylene], PBISP; from 150 to 620 K using differential scanning calorimetry. These new data, along with the prior ATHAS (Laboratory for Advanced Thermal Analysis, University of Tennessee) recommended experimental heat capacities for three aliphatic polysulphones: poly(1-propene sulphone), P1PS (20–300 K); poly(1-butene sulphone), P1BS (100–300 K); poly(1-hexene sulphone), P1HS (20–300 K), were fitted to an approximate frequency spectrum below their respective glass transition temperatures. The ATHAS computation scheme was used to compute the heat capacities that arise from these vibrations from 0.1 to 1000 K. The ϑ 1 -temperature changed from 685 K for P1PS to 587 K for P1HS while for PPES and PBISP much higher values (799.5 K and 777.8 K) than the other phenylene polymers analysed at ATHAS, were obtained. Using these data and the smoothed experimental liquid heat capacities, the glass transition temperatures for PAS, PPES and PBISP were obtained at 492.6, 497.4 and 458.2 K. The corresponding values for ΔC p were 18.1, 37.7 and 126.6 J K −1 mol −1 , respectively.

Analysis of the thermal properties and motion in crystalline trans-1,4-poly(butadiene)

Abstract A new analysis of the disordering transition of semicrystalline trans -1,4-poly(butadiene) is presented, based on an improved calculation of the transition enthalpy from the crystal form I to the mesophase II (condis phase). In the past it had been overlooked that the experimental heat capacity starts to deviate more than one hundred kelvins below the peak temperature of the disordering transition temperature T d from that contributed by the amorphous fraction and the crystal. An assessment of the additional entropy of disordering at lower temperature suggests that by the time the glass transition is reached on cooling, all the mesophase is converted to the fully ordered crystal form I .

Motion and Disorder in the Plastic Crystal of the C70 Complex with Toluene by Solid State NMR and Thermal Analysis

Abstract Molecular motion and disorder in a C70 toluene complex of molar ratio 1/1 have been analyzed by obtaining 13C NMR powder patterns and magic angle spinning spectra over the temperature range from 150 to 373 K, as well as by DSC measurement of heat capacity and heats of transition from 120 to 560 K. The C70 molecules start some orientational motion below 150 K. The well-known transitions of C70 between 260 and 350 K are suppressed in the complex, but the toluene molecules contribute a liquid-like heat capacity above 178 K. Evaporation of the toluene occurs sharply at 446 K with a heat of decomposition of 36.1 kJ/mol (2.9 kJ/mol more than the heat of evaporation of pure toluene and 62 K higher than the boiling temperature of toluene). At room temperature and above, pure C70 has a rotational correlation time of less than 100 μs, while for the toluene-containing C70 the motion is much less. The toluene molecules are closer to the equatorial “belt” of the C70 prolate spheroid and prohibit the C70 molec...